Consider the number line with the plotted square roots.

Question

Inspect the number line. Which square roots have a difference of about 0.5?

(1 point)
Responses

19−−√
and 24−−√
square root of 19 and square root of 24

11−−√
and 14−−√
square root of 11 and square root of 14

11−−√
and 19−−√
square root of 11 and square root of 19

14−−√
and 19−−√

Answer 1

To find which square roots have a difference of about 0.5, we can estimate the values of the square roots:

1. \(\sqrt{19} \approx 4.36\)
2. \(\sqrt{24} \approx 4.9\)

The difference \(\sqrt{24} - \sqrt{19} \approx 4.9 - 4.36 = 0.54\), which is about 0.5.

Now, let's check the other pairs:

3. \(\sqrt{11} \approx 3.32\)
4. \(\sqrt{14} \approx 3.74\)

The difference \(\sqrt{14} - \sqrt{11} \approx 3.74 - 3.32 = 0.42\), which is less than 0.5.

5. \(\sqrt{11} \) and \(\sqrt{19}\):

   • Difference: \( \sqrt{19} - \sqrt{11} \approx 4.36 - 3.32 = 1.04\)

6. \(\sqrt{14} \) and \(\sqrt{19}\):

   • Difference: \(\sqrt{19} - \sqrt{14} \approx 4.36 - 3.74 = 0.62\)

From these calculations, the pair that has a difference of about 0.5 is:

• \(\sqrt{19}\) and \(\sqrt{24}\)

So the correct response is:

\(\sqrt{19}\) and \(\sqrt{24}\).